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## Functional method for quantum ferromagnet and non-magnon dynamics at low temperatures

A review of our recent results on the spin valve effect is presented. We have used a theoretically proposed spin switch design F1/F2/S comprising a ferromagnetic bilayer (F1/F2) as a ferromagnetic component, and an ordinary superconductor (S) as the second interface component. Based on it we have prepared and studied in detail a set of multilayers CoO*x*/Fe1/Cu/Fe2/S (S=In or Pb). In these heterostructures we have realized for the first time a full spin switch effect for the superconducting current, have observed its sign-changing oscillating behavior as a function of the Fe2-layer thickness and finally have obtained direct evidence for the long-range triplet superconductivity arising due to noncollinearity of the magnetizations of the Fe1 and Fe2 layers.

We have studied the proximity-induced superconducting triplet pairing in CoO_x/Py1/Cu/Py2/Cu/Pb spin-valve structure (where Py = Ni_{0.81}Fe_{0.19}). By optimizing the parameters of this structure we found a triplet channel assisted full switching between the normal and superconducting states. To observe an "isolated" triplet spin-valve effect we exploited the oscillatory feature of the magnitude of the ordinary spin-valve effect ΔTc in the dependence of the Py2-layer thickness dPy2. We determined the value of dPy2 at which ΔTc caused by the ordinary spin-valve effect (the difference in the superconducting transition temperature Tc between the antiparallel and parallel mutual orientation of magnetizations of the Py1 and Py2 layers) is suppressed. For such a sample a "pure" triplet spin-valve effect which causes the minimum in Tc at the orthogonal configuration of magnetizations has been observed.

We report magnetic and superconducting properties of the modified spin valve system CoOx/Fe1/Cu/Fe2/Cu/Pb. Introduction of a Cu interlayer between Fe2 and Pb layers prevents material interdiffusion process, increases the Fe2/Pb interface transparency, stabilizes and enhances properties of the system. This allowed us to perform a comprehensive study of such heterostructures and to present theoretical description of the superconducting spin valve effect and of the manifestation of the long-range triplet component of the superconducting condensate.

The dynamics of a two-component Davydov-Scott (DS) soliton with a small mismatch of the initial location or velocity of the high-frequency (HF) component was investigated within the framework of the Zakharov-type system of two coupled equations for the HF and low-frequency (LF) fields. In this system, the HF field is described by the linear Schrödinger equation with the potential generated by the LF component varying in time and space. The LF component in this system is described by the Korteweg-de Vries equation with a term of quadratic influence of the HF field on the LF field. The frequency of the DS soliton`s component oscillation was found analytically using the balance equation. The perturbed DS soliton was shown to be stable. The analytical results were confirmed by numerical simulations.

Radiation conditions are described for various space regions, radiation-induced effects in spacecraft materials and equipment components are considered and information on theoretical, computational, and experimental methods for studying radiation effects are presented. The peculiarities of radiation effects on nanostructures and some problems related to modeling and radiation testing of such structures are considered.

Let k be a field of characteristic zero, let G be a connected reductive algebraic group over k and let g be its Lie algebra. Let k(G), respectively, k(g), be the field of k- rational functions on G, respectively, g. The conjugation action of G on itself induces the adjoint action of G on g. We investigate the question whether or not the field extensions k(G)/k(G)^G and k(g)/k(g)^G are purely transcendental. We show that the answer is the same for k(G)/k(G)^G and k(g)/k(g)^G, and reduce the problem to the case where G is simple. For simple groups we show that the answer is positive if G is split of type A_n or C_n, and negative for groups of other types, except possibly G_2. A key ingredient in the proof of the negative result is a recent formula for the unramified Brauer group of a homogeneous space with connected stabilizers. As a byproduct of our investigation we give an affirmative answer to a question of Grothendieck about the existence of a rational section of the categorical quotient morphism for the conjugating action of G on itself.

This proceedings publication is a compilation of selected contributions from the “Third International Conference on the Dynamics of Information Systems” which took place at the University of Florida, Gainesville, February 16–18, 2011. The purpose of this conference was to bring together scientists and engineers from industry, government, and academia in order to exchange new discoveries and results in a broad range of topics relevant to the theory and practice of dynamics of information systems. Dynamics of Information Systems: Mathematical Foundation presents state-of-the art research and is intended for graduate students and researchers interested in some of the most recent discoveries in information theory and dynamical systems. Scientists in other disciplines may also benefit from the applications of new developments to their own area of study.

Let G be a connected semisimple algebraic group over an algebraically closed field k. In 1965 Steinberg proved that if G is simply connected, then in G there exists a closed irreducible cross-section of the set of closures of regular conjugacy classes. We prove that in arbitrary G such a cross-section exists if and only if the universal covering isogeny Ĝ → G is bijective; this answers Grothendieck's question cited in the epigraph. In particular, for char k = 0, the converse to Steinberg's theorem holds. The existence of a cross-section in G implies, at least for char k = 0, that the algebra k[G]G of class functions on G is generated by rk G elements. We describe, for arbitrary G, a minimal generating set of k[G]G and that of the representation ring of G and answer two Grothendieck's questions on constructing generating sets of k[G]G. We prove the existence of a rational (i.e., local) section of the quotient morphism for arbitrary G and the existence of a rational cross-section in G (for char k = 0, this has been proved earlier); this answers the other question cited in the epigraph. We also prove that the existence of a rational section is equivalent to the existence of a rational W-equivariant map T- - - >G/T where T is a maximal torus of G and W the Weyl group.